Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [275,2,Mod(1,275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(275, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("275.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 275 = 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 275.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(2.19588605559\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 275.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61803 | −1.14412 | −0.572061 | − | 0.820211i | \(-0.693856\pi\) | ||||
−0.572061 | + | 0.820211i | \(0.693856\pi\) | |||||||
\(3\) | −2.61803 | −1.51152 | −0.755761 | − | 0.654847i | \(-0.772733\pi\) | ||||
−0.755761 | + | 0.654847i | \(0.772733\pi\) | |||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.23607 | 1.72937 | ||||||||
\(7\) | 2.85410 | 1.07875 | 0.539375 | − | 0.842066i | \(-0.318661\pi\) | ||||
0.539375 | + | 0.842066i | \(0.318661\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 3.85410 | 1.28470 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.61803 | −0.467086 | ||||||||
\(13\) | −6.23607 | −1.72957 | −0.864787 | − | 0.502139i | \(-0.832547\pi\) | ||||
−0.864787 | + | 0.502139i | \(0.832547\pi\) | |||||||
\(14\) | −4.61803 | −1.23422 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 0.618034 | 0.149895 | 0.0749476 | − | 0.997187i | \(-0.476121\pi\) | ||||
0.0749476 | + | 0.997187i | \(0.476121\pi\) | |||||||
\(18\) | −6.23607 | −1.46986 | ||||||||
\(19\) | −6.70820 | −1.53897 | −0.769484 | − | 0.638666i | \(-0.779486\pi\) | ||||
−0.769484 | + | 0.638666i | \(0.779486\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.47214 | −1.63055 | ||||||||
\(22\) | −1.61803 | −0.344966 | ||||||||
\(23\) | 4.09017 | 0.852859 | 0.426430 | − | 0.904521i | \(-0.359771\pi\) | ||||
0.426430 | + | 0.904521i | \(0.359771\pi\) | |||||||
\(24\) | −5.85410 | −1.19496 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 10.0902 | 1.97885 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 1.76393 | 0.333352 | ||||||||
\(29\) | −1.38197 | −0.256625 | −0.128312 | − | 0.991734i | \(-0.540956\pi\) | ||||
−0.128312 | + | 0.991734i | \(0.540956\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | 3.38197 | 0.597853 | ||||||||
\(33\) | −2.61803 | −0.455741 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.38197 | 0.396994 | ||||||||
\(37\) | −10.2361 | −1.68280 | −0.841400 | − | 0.540413i | \(-0.818268\pi\) | ||||
−0.841400 | + | 0.540413i | \(0.818268\pi\) | |||||||
\(38\) | 10.8541 | 1.76077 | ||||||||
\(39\) | 16.3262 | 2.61429 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 12.0902 | 1.86555 | ||||||||
\(43\) | 6.00000 | 0.914991 | 0.457496 | − | 0.889212i | \(-0.348747\pi\) | ||||
0.457496 | + | 0.889212i | \(0.348747\pi\) | |||||||
\(44\) | 0.618034 | 0.0931721 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.61803 | −0.975776 | ||||||||
\(47\) | −11.9443 | −1.74225 | −0.871126 | − | 0.491060i | \(-0.836609\pi\) | ||||
−0.871126 | + | 0.491060i | \(0.836609\pi\) | |||||||
\(48\) | 12.7082 | 1.83427 | ||||||||
\(49\) | 1.14590 | 0.163700 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.61803 | −0.226570 | ||||||||
\(52\) | −3.85410 | −0.534468 | ||||||||
\(53\) | −9.32624 | −1.28106 | −0.640529 | − | 0.767934i | \(-0.721285\pi\) | ||||
−0.640529 | + | 0.767934i | \(0.721285\pi\) | |||||||
\(54\) | 3.61803 | 0.492352 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.38197 | 0.852826 | ||||||||
\(57\) | 17.5623 | 2.32618 | ||||||||
\(58\) | 2.23607 | 0.293610 | ||||||||
\(59\) | 0.527864 | 0.0687220 | 0.0343610 | − | 0.999409i | \(-0.489060\pi\) | ||||
0.0343610 | + | 0.999409i | \(0.489060\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0901699 | 0.0115451 | 0.00577254 | − | 0.999983i | \(-0.498163\pi\) | ||||
0.00577254 | + | 0.999983i | \(0.498163\pi\) | |||||||
\(62\) | 4.85410 | 0.616472 | ||||||||
\(63\) | 11.0000 | 1.38587 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.23607 | 0.521424 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | 0.381966 | 0.0463202 | ||||||||
\(69\) | −10.7082 | −1.28912 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.18034 | 0.970828 | 0.485414 | − | 0.874284i | \(-0.338669\pi\) | ||||
0.485414 | + | 0.874284i | \(0.338669\pi\) | |||||||
\(72\) | 8.61803 | 1.01565 | ||||||||
\(73\) | −10.3820 | −1.21512 | −0.607559 | − | 0.794275i | \(-0.707851\pi\) | ||||
−0.607559 | + | 0.794275i | \(0.707851\pi\) | |||||||
\(74\) | 16.5623 | 1.92533 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.14590 | −0.475567 | ||||||||
\(77\) | 2.85410 | 0.325255 | ||||||||
\(78\) | −26.4164 | −2.99107 | ||||||||
\(79\) | 5.85410 | 0.658638 | 0.329319 | − | 0.944219i | \(-0.393181\pi\) | ||||
0.329319 | + | 0.944219i | \(0.393181\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.70820 | −0.634245 | ||||||||
\(82\) | 4.85410 | 0.536046 | ||||||||
\(83\) | 10.1459 | 1.11366 | 0.556828 | − | 0.830627i | \(-0.312018\pi\) | ||||
0.556828 | + | 0.830627i | \(0.312018\pi\) | |||||||
\(84\) | −4.61803 | −0.503869 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.70820 | −1.04686 | ||||||||
\(87\) | 3.61803 | 0.387894 | ||||||||
\(88\) | 2.23607 | 0.238366 | ||||||||
\(89\) | −6.90983 | −0.732441 | −0.366220 | − | 0.930528i | \(-0.619348\pi\) | ||||
−0.366220 | + | 0.930528i | \(0.619348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.7984 | −1.86578 | ||||||||
\(92\) | 2.52786 | 0.263548 | ||||||||
\(93\) | 7.85410 | 0.814432 | ||||||||
\(94\) | 19.3262 | 1.99335 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.85410 | −0.903668 | ||||||||
\(97\) | −1.61803 | −0.164286 | −0.0821432 | − | 0.996621i | \(-0.526176\pi\) | ||||
−0.0821432 | + | 0.996621i | \(0.526176\pi\) | |||||||
\(98\) | −1.85410 | −0.187293 | ||||||||
\(99\) | 3.85410 | 0.387352 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.09017 | −0.605995 | −0.302997 | − | 0.952991i | \(-0.597987\pi\) | ||||
−0.302997 | + | 0.952991i | \(0.597987\pi\) | |||||||
\(102\) | 2.61803 | 0.259224 | ||||||||
\(103\) | −5.38197 | −0.530301 | −0.265150 | − | 0.964207i | \(-0.585422\pi\) | ||||
−0.265150 | + | 0.964207i | \(0.585422\pi\) | |||||||
\(104\) | −13.9443 | −1.36735 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.0902 | 1.46569 | ||||||||
\(107\) | 4.23607 | 0.409516 | 0.204758 | − | 0.978813i | \(-0.434359\pi\) | ||||
0.204758 | + | 0.978813i | \(0.434359\pi\) | |||||||
\(108\) | −1.38197 | −0.132980 | ||||||||
\(109\) | −3.09017 | −0.295985 | −0.147992 | − | 0.988989i | \(-0.547281\pi\) | ||||
−0.147992 | + | 0.988989i | \(0.547281\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.7984 | 2.54359 | ||||||||
\(112\) | −13.8541 | −1.30909 | ||||||||
\(113\) | 11.6525 | 1.09617 | 0.548086 | − | 0.836422i | \(-0.315357\pi\) | ||||
0.548086 | + | 0.836422i | \(0.315357\pi\) | |||||||
\(114\) | −28.4164 | −2.66144 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.854102 | −0.0793014 | ||||||||
\(117\) | −24.0344 | −2.22198 | ||||||||
\(118\) | −0.854102 | −0.0786265 | ||||||||
\(119\) | 1.76393 | 0.161699 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.145898 | −0.0132090 | ||||||||
\(123\) | 7.85410 | 0.708181 | ||||||||
\(124\) | −1.85410 | −0.166503 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −17.7984 | −1.58561 | ||||||||
\(127\) | 0.618034 | 0.0548416 | 0.0274208 | − | 0.999624i | \(-0.491271\pi\) | ||||
0.0274208 | + | 0.999624i | \(0.491271\pi\) | |||||||
\(128\) | −13.6180 | −1.20368 | ||||||||
\(129\) | −15.7082 | −1.38303 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0902 | 0.881582 | 0.440791 | − | 0.897610i | \(-0.354698\pi\) | ||||
0.440791 | + | 0.897610i | \(0.354698\pi\) | |||||||
\(132\) | −1.61803 | −0.140832 | ||||||||
\(133\) | −19.1459 | −1.66016 | ||||||||
\(134\) | 12.9443 | 1.11821 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.38197 | 0.118503 | ||||||||
\(137\) | −5.56231 | −0.475220 | −0.237610 | − | 0.971361i | \(-0.576364\pi\) | ||||
−0.237610 | + | 0.971361i | \(0.576364\pi\) | |||||||
\(138\) | 17.3262 | 1.47491 | ||||||||
\(139\) | −3.29180 | −0.279206 | −0.139603 | − | 0.990208i | \(-0.544583\pi\) | ||||
−0.139603 | + | 0.990208i | \(0.544583\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 31.2705 | 2.63345 | ||||||||
\(142\) | −13.2361 | −1.11075 | ||||||||
\(143\) | −6.23607 | −0.521486 | ||||||||
\(144\) | −18.7082 | −1.55902 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.7984 | 1.39024 | ||||||||
\(147\) | −3.00000 | −0.247436 | ||||||||
\(148\) | −6.32624 | −0.520014 | ||||||||
\(149\) | −8.94427 | −0.732743 | −0.366372 | − | 0.930469i | \(-0.619400\pi\) | ||||
−0.366372 | + | 0.930469i | \(0.619400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.00000 | −0.244137 | −0.122068 | − | 0.992522i | \(-0.538953\pi\) | ||||
−0.122068 | + | 0.992522i | \(0.538953\pi\) | |||||||
\(152\) | −15.0000 | −1.21666 | ||||||||
\(153\) | 2.38197 | 0.192571 | ||||||||
\(154\) | −4.61803 | −0.372132 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.0902 | 0.807860 | ||||||||
\(157\) | 5.41641 | 0.432276 | 0.216138 | − | 0.976363i | \(-0.430654\pi\) | ||||
0.216138 | + | 0.976363i | \(0.430654\pi\) | |||||||
\(158\) | −9.47214 | −0.753563 | ||||||||
\(159\) | 24.4164 | 1.93635 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.6738 | 0.920021 | ||||||||
\(162\) | 9.23607 | 0.725654 | ||||||||
\(163\) | 6.85410 | 0.536855 | 0.268427 | − | 0.963300i | \(-0.413496\pi\) | ||||
0.268427 | + | 0.963300i | \(0.413496\pi\) | |||||||
\(164\) | −1.85410 | −0.144781 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.4164 | −1.27416 | ||||||||
\(167\) | 5.29180 | 0.409491 | 0.204746 | − | 0.978815i | \(-0.434363\pi\) | ||||
0.204746 | + | 0.978815i | \(0.434363\pi\) | |||||||
\(168\) | −16.7082 | −1.28907 | ||||||||
\(169\) | 25.8885 | 1.99143 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −25.8541 | −1.97711 | ||||||||
\(172\) | 3.70820 | 0.282748 | ||||||||
\(173\) | 5.47214 | 0.416039 | 0.208019 | − | 0.978125i | \(-0.433298\pi\) | ||||
0.208019 | + | 0.978125i | \(0.433298\pi\) | |||||||
\(174\) | −5.85410 | −0.443798 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.85410 | −0.365892 | ||||||||
\(177\) | −1.38197 | −0.103875 | ||||||||
\(178\) | 11.1803 | 0.838002 | ||||||||
\(179\) | −13.6180 | −1.01786 | −0.508930 | − | 0.860808i | \(-0.669959\pi\) | ||||
−0.508930 | + | 0.860808i | \(0.669959\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.09017 | −0.452679 | −0.226339 | − | 0.974049i | \(-0.572676\pi\) | ||||
−0.226339 | + | 0.974049i | \(0.572676\pi\) | |||||||
\(182\) | 28.7984 | 2.13468 | ||||||||
\(183\) | −0.236068 | −0.0174506 | ||||||||
\(184\) | 9.14590 | 0.674245 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −12.7082 | −0.931811 | ||||||||
\(187\) | 0.618034 | 0.0451951 | ||||||||
\(188\) | −7.38197 | −0.538385 | ||||||||
\(189\) | −6.38197 | −0.464220 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.0902 | −1.52603 | −0.763016 | − | 0.646380i | \(-0.776282\pi\) | ||||
−0.763016 | + | 0.646380i | \(0.776282\pi\) | |||||||
\(192\) | −11.0902 | −0.800364 | ||||||||
\(193\) | −12.9443 | −0.931749 | −0.465875 | − | 0.884851i | \(-0.654260\pi\) | ||||
−0.465875 | + | 0.884851i | \(0.654260\pi\) | |||||||
\(194\) | 2.61803 | 0.187964 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.708204 | 0.0505860 | ||||||||
\(197\) | 20.0902 | 1.43137 | 0.715683 | − | 0.698426i | \(-0.246116\pi\) | ||||
0.715683 | + | 0.698426i | \(0.246116\pi\) | |||||||
\(198\) | −6.23607 | −0.443178 | ||||||||
\(199\) | −3.09017 | −0.219056 | −0.109528 | − | 0.993984i | \(-0.534934\pi\) | ||||
−0.109528 | + | 0.993984i | \(0.534934\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.9443 | 1.47730 | ||||||||
\(202\) | 9.85410 | 0.693332 | ||||||||
\(203\) | −3.94427 | −0.276834 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.70820 | 0.606729 | ||||||||
\(207\) | 15.7639 | 1.09567 | ||||||||
\(208\) | 30.2705 | 2.09888 | ||||||||
\(209\) | −6.70820 | −0.464016 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0000 | 1.17033 | 0.585164 | − | 0.810915i | \(-0.301030\pi\) | ||||
0.585164 | + | 0.810915i | \(0.301030\pi\) | |||||||
\(212\) | −5.76393 | −0.395868 | ||||||||
\(213\) | −21.4164 | −1.46743 | ||||||||
\(214\) | −6.85410 | −0.468537 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | −8.56231 | −0.581247 | ||||||||
\(218\) | 5.00000 | 0.338643 | ||||||||
\(219\) | 27.1803 | 1.83668 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.85410 | −0.259255 | ||||||||
\(222\) | −43.3607 | −2.91018 | ||||||||
\(223\) | −16.8885 | −1.13094 | −0.565470 | − | 0.824769i | \(-0.691305\pi\) | ||||
−0.565470 | + | 0.824769i | \(0.691305\pi\) | |||||||
\(224\) | 9.65248 | 0.644933 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.8541 | −1.25416 | ||||||||
\(227\) | 24.0344 | 1.59522 | 0.797611 | − | 0.603172i | \(-0.206097\pi\) | ||||
0.797611 | + | 0.603172i | \(0.206097\pi\) | |||||||
\(228\) | 10.8541 | 0.718830 | ||||||||
\(229\) | 12.0344 | 0.795258 | 0.397629 | − | 0.917546i | \(-0.369833\pi\) | ||||
0.397629 | + | 0.917546i | \(0.369833\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.47214 | −0.491630 | ||||||||
\(232\) | −3.09017 | −0.202880 | ||||||||
\(233\) | −15.5066 | −1.01587 | −0.507935 | − | 0.861395i | \(-0.669591\pi\) | ||||
−0.507935 | + | 0.861395i | \(0.669591\pi\) | |||||||
\(234\) | 38.8885 | 2.54222 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.326238 | 0.0212363 | ||||||||
\(237\) | −15.3262 | −0.995546 | ||||||||
\(238\) | −2.85410 | −0.185004 | ||||||||
\(239\) | 6.38197 | 0.412815 | 0.206408 | − | 0.978466i | \(-0.433823\pi\) | ||||
0.206408 | + | 0.978466i | \(0.433823\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.2705 | 1.37015 | 0.685077 | − | 0.728471i | \(-0.259769\pi\) | ||||
0.685077 | + | 0.728471i | \(0.259769\pi\) | |||||||
\(242\) | −1.61803 | −0.104011 | ||||||||
\(243\) | 21.6525 | 1.38901 | ||||||||
\(244\) | 0.0557281 | 0.00356763 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −12.7082 | −0.810245 | ||||||||
\(247\) | 41.8328 | 2.66176 | ||||||||
\(248\) | −6.70820 | −0.425971 | ||||||||
\(249\) | −26.5623 | −1.68332 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.2705 | −1.72130 | −0.860650 | − | 0.509198i | \(-0.829942\pi\) | ||||
−0.860650 | + | 0.509198i | \(0.829942\pi\) | |||||||
\(252\) | 6.79837 | 0.428257 | ||||||||
\(253\) | 4.09017 | 0.257147 | ||||||||
\(254\) | −1.00000 | −0.0627456 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 10.9443 | 0.682685 | 0.341342 | − | 0.939939i | \(-0.389118\pi\) | ||||
0.341342 | + | 0.939939i | \(0.389118\pi\) | |||||||
\(258\) | 25.4164 | 1.58236 | ||||||||
\(259\) | −29.2148 | −1.81532 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.32624 | −0.329686 | ||||||||
\(262\) | −16.3262 | −1.00864 | ||||||||
\(263\) | 21.0000 | 1.29492 | 0.647458 | − | 0.762101i | \(-0.275832\pi\) | ||||
0.647458 | + | 0.762101i | \(0.275832\pi\) | |||||||
\(264\) | −5.85410 | −0.360295 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 30.9787 | 1.89943 | ||||||||
\(267\) | 18.0902 | 1.10710 | ||||||||
\(268\) | −4.94427 | −0.302019 | ||||||||
\(269\) | 30.3262 | 1.84902 | 0.924512 | − | 0.381154i | \(-0.124473\pi\) | ||||
0.924512 | + | 0.381154i | \(0.124473\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.1803 | 0.800649 | 0.400324 | − | 0.916374i | \(-0.368897\pi\) | ||||
0.400324 | + | 0.916374i | \(0.368897\pi\) | |||||||
\(272\) | −3.00000 | −0.181902 | ||||||||
\(273\) | 46.5967 | 2.82016 | ||||||||
\(274\) | 9.00000 | 0.543710 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.61803 | −0.398359 | ||||||||
\(277\) | 11.4721 | 0.689294 | 0.344647 | − | 0.938732i | \(-0.387999\pi\) | ||||
0.344647 | + | 0.938732i | \(0.387999\pi\) | |||||||
\(278\) | 5.32624 | 0.319447 | ||||||||
\(279\) | −11.5623 | −0.692217 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.3607 | −1.51289 | −0.756446 | − | 0.654057i | \(-0.773066\pi\) | ||||
−0.756446 | + | 0.654057i | \(0.773066\pi\) | |||||||
\(282\) | −50.5967 | −3.01299 | ||||||||
\(283\) | 7.38197 | 0.438812 | 0.219406 | − | 0.975634i | \(-0.429588\pi\) | ||||
0.219406 | + | 0.975634i | \(0.429588\pi\) | |||||||
\(284\) | 5.05573 | 0.300002 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.0902 | 0.596644 | ||||||||
\(287\) | −8.56231 | −0.505417 | ||||||||
\(288\) | 13.0344 | 0.768062 | ||||||||
\(289\) | −16.6180 | −0.977531 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.23607 | 0.248323 | ||||||||
\(292\) | −6.41641 | −0.375492 | ||||||||
\(293\) | 23.8885 | 1.39558 | 0.697792 | − | 0.716301i | \(-0.254166\pi\) | ||||
0.697792 | + | 0.716301i | \(0.254166\pi\) | |||||||
\(294\) | 4.85410 | 0.283097 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −22.8885 | −1.33037 | ||||||||
\(297\) | −2.23607 | −0.129750 | ||||||||
\(298\) | 14.4721 | 0.838348 | ||||||||
\(299\) | −25.5066 | −1.47508 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.1246 | 0.987046 | ||||||||
\(302\) | 4.85410 | 0.279322 | ||||||||
\(303\) | 15.9443 | 0.915974 | ||||||||
\(304\) | 32.5623 | 1.86758 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.85410 | −0.220324 | ||||||||
\(307\) | −33.4508 | −1.90914 | −0.954570 | − | 0.297985i | \(-0.903685\pi\) | ||||
−0.954570 | + | 0.297985i | \(0.903685\pi\) | |||||||
\(308\) | 1.76393 | 0.100509 | ||||||||
\(309\) | 14.0902 | 0.801562 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.1803 | −1.08762 | −0.543809 | − | 0.839209i | \(-0.683018\pi\) | ||||
−0.543809 | + | 0.839209i | \(0.683018\pi\) | |||||||
\(312\) | 36.5066 | 2.06678 | ||||||||
\(313\) | 3.23607 | 0.182913 | 0.0914567 | − | 0.995809i | \(-0.470848\pi\) | ||||
0.0914567 | + | 0.995809i | \(0.470848\pi\) | |||||||
\(314\) | −8.76393 | −0.494577 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.61803 | 0.203530 | ||||||||
\(317\) | −16.6180 | −0.933362 | −0.466681 | − | 0.884426i | \(-0.654550\pi\) | ||||
−0.466681 | + | 0.884426i | \(0.654550\pi\) | |||||||
\(318\) | −39.5066 | −2.21542 | ||||||||
\(319\) | −1.38197 | −0.0773752 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.0902 | −0.618993 | ||||||||
\(322\) | −18.8885 | −1.05262 | ||||||||
\(323\) | −4.14590 | −0.230684 | ||||||||
\(324\) | −3.52786 | −0.195992 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.0902 | −0.614228 | ||||||||
\(327\) | 8.09017 | 0.447387 | ||||||||
\(328\) | −6.70820 | −0.370399 | ||||||||
\(329\) | −34.0902 | −1.87945 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.1803 | −1.05425 | −0.527123 | − | 0.849789i | \(-0.676729\pi\) | ||||
−0.527123 | + | 0.849789i | \(0.676729\pi\) | |||||||
\(332\) | 6.27051 | 0.344139 | ||||||||
\(333\) | −39.4508 | −2.16189 | ||||||||
\(334\) | −8.56231 | −0.468509 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 36.2705 | 1.97872 | ||||||||
\(337\) | −1.41641 | −0.0771567 | −0.0385783 | − | 0.999256i | \(-0.512283\pi\) | ||||
−0.0385783 | + | 0.999256i | \(0.512283\pi\) | |||||||
\(338\) | −41.8885 | −2.27844 | ||||||||
\(339\) | −30.5066 | −1.65689 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.00000 | −0.162459 | ||||||||
\(342\) | 41.8328 | 2.26206 | ||||||||
\(343\) | −16.7082 | −0.902158 | ||||||||
\(344\) | 13.4164 | 0.723364 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.85410 | −0.475999 | ||||||||
\(347\) | −20.5623 | −1.10384 | −0.551921 | − | 0.833896i | \(-0.686105\pi\) | ||||
−0.551921 | + | 0.833896i | \(0.686105\pi\) | |||||||
\(348\) | 2.23607 | 0.119866 | ||||||||
\(349\) | 21.8328 | 1.16868 | 0.584342 | − | 0.811508i | \(-0.301353\pi\) | ||||
0.584342 | + | 0.811508i | \(0.301353\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.9443 | 0.744290 | ||||||||
\(352\) | 3.38197 | 0.180259 | ||||||||
\(353\) | −21.3607 | −1.13691 | −0.568457 | − | 0.822713i | \(-0.692459\pi\) | ||||
−0.568457 | + | 0.822713i | \(0.692459\pi\) | |||||||
\(354\) | 2.23607 | 0.118846 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.27051 | −0.226337 | ||||||||
\(357\) | −4.61803 | −0.244412 | ||||||||
\(358\) | 22.0344 | 1.16456 | ||||||||
\(359\) | −4.47214 | −0.236030 | −0.118015 | − | 0.993012i | \(-0.537653\pi\) | ||||
−0.118015 | + | 0.993012i | \(0.537653\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.0000 | 1.36842 | ||||||||
\(362\) | 9.85410 | 0.517920 | ||||||||
\(363\) | −2.61803 | −0.137411 | ||||||||
\(364\) | −11.0000 | −0.576557 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.381966 | 0.0199657 | ||||||||
\(367\) | −7.14590 | −0.373013 | −0.186506 | − | 0.982454i | \(-0.559717\pi\) | ||||
−0.186506 | + | 0.982454i | \(0.559717\pi\) | |||||||
\(368\) | −19.8541 | −1.03497 | ||||||||
\(369\) | −11.5623 | −0.601910 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.6180 | −1.38194 | ||||||||
\(372\) | 4.85410 | 0.251673 | ||||||||
\(373\) | −2.81966 | −0.145996 | −0.0729982 | − | 0.997332i | \(-0.523257\pi\) | ||||
−0.0729982 | + | 0.997332i | \(0.523257\pi\) | |||||||
\(374\) | −1.00000 | −0.0517088 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −26.7082 | −1.37737 | ||||||||
\(377\) | 8.61803 | 0.443851 | ||||||||
\(378\) | 10.3262 | 0.531124 | ||||||||
\(379\) | −17.7639 | −0.912472 | −0.456236 | − | 0.889859i | \(-0.650803\pi\) | ||||
−0.456236 | + | 0.889859i | \(0.650803\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.61803 | −0.0828944 | ||||||||
\(382\) | 34.1246 | 1.74597 | ||||||||
\(383\) | −5.05573 | −0.258336 | −0.129168 | − | 0.991623i | \(-0.541231\pi\) | ||||
−0.129168 | + | 0.991623i | \(0.541231\pi\) | |||||||
\(384\) | 35.6525 | 1.81938 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.9443 | 1.06604 | ||||||||
\(387\) | 23.1246 | 1.17549 | ||||||||
\(388\) | −1.00000 | −0.0507673 | ||||||||
\(389\) | 5.52786 | 0.280274 | 0.140137 | − | 0.990132i | \(-0.455246\pi\) | ||||
0.140137 | + | 0.990132i | \(0.455246\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.52786 | 0.127840 | ||||||||
\(392\) | 2.56231 | 0.129416 | ||||||||
\(393\) | −26.4164 | −1.33253 | ||||||||
\(394\) | −32.5066 | −1.63766 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.38197 | 0.119698 | ||||||||
\(397\) | −14.9098 | −0.748303 | −0.374151 | − | 0.927368i | \(-0.622066\pi\) | ||||
−0.374151 | + | 0.927368i | \(0.622066\pi\) | |||||||
\(398\) | 5.00000 | 0.250627 | ||||||||
\(399\) | 50.1246 | 2.50937 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.3607 | 1.71589 | 0.857945 | − | 0.513741i | \(-0.171741\pi\) | ||||
0.857945 | + | 0.513741i | \(0.171741\pi\) | |||||||
\(402\) | −33.8885 | −1.69021 | ||||||||
\(403\) | 18.7082 | 0.931922 | ||||||||
\(404\) | −3.76393 | −0.187263 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.38197 | 0.316732 | ||||||||
\(407\) | −10.2361 | −0.507383 | ||||||||
\(408\) | −3.61803 | −0.179119 | ||||||||
\(409\) | 20.1246 | 0.995098 | 0.497549 | − | 0.867436i | \(-0.334233\pi\) | ||||
0.497549 | + | 0.867436i | \(0.334233\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.5623 | 0.718306 | ||||||||
\(412\) | −3.32624 | −0.163872 | ||||||||
\(413\) | 1.50658 | 0.0741338 | ||||||||
\(414\) | −25.5066 | −1.25358 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −21.0902 | −1.03403 | ||||||||
\(417\) | 8.61803 | 0.422027 | ||||||||
\(418\) | 10.8541 | 0.530891 | ||||||||
\(419\) | 21.1803 | 1.03473 | 0.517364 | − | 0.855766i | \(-0.326913\pi\) | ||||
0.517364 | + | 0.855766i | \(0.326913\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.2705 | −0.598028 | −0.299014 | − | 0.954249i | \(-0.596658\pi\) | ||||
−0.299014 | + | 0.954249i | \(0.596658\pi\) | |||||||
\(422\) | −27.5066 | −1.33900 | ||||||||
\(423\) | −46.0344 | −2.23827 | ||||||||
\(424\) | −20.8541 | −1.01276 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 34.6525 | 1.67892 | ||||||||
\(427\) | 0.257354 | 0.0124542 | ||||||||
\(428\) | 2.61803 | 0.126547 | ||||||||
\(429\) | 16.3262 | 0.788238 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.819660 | 0.0394816 | 0.0197408 | − | 0.999805i | \(-0.493716\pi\) | ||||
0.0197408 | + | 0.999805i | \(0.493716\pi\) | |||||||
\(432\) | 10.8541 | 0.522218 | ||||||||
\(433\) | 18.8885 | 0.907725 | 0.453863 | − | 0.891072i | \(-0.350046\pi\) | ||||
0.453863 | + | 0.891072i | \(0.350046\pi\) | |||||||
\(434\) | 13.8541 | 0.665018 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.90983 | −0.0914643 | ||||||||
\(437\) | −27.4377 | −1.31252 | ||||||||
\(438\) | −43.9787 | −2.10138 | ||||||||
\(439\) | −0.729490 | −0.0348167 | −0.0174083 | − | 0.999848i | \(-0.505542\pi\) | ||||
−0.0174083 | + | 0.999848i | \(0.505542\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.41641 | 0.210305 | ||||||||
\(442\) | 6.23607 | 0.296620 | ||||||||
\(443\) | 36.6525 | 1.74141 | 0.870706 | − | 0.491804i | \(-0.163662\pi\) | ||||
0.870706 | + | 0.491804i | \(0.163662\pi\) | |||||||
\(444\) | 16.5623 | 0.786012 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 27.3262 | 1.29393 | ||||||||
\(447\) | 23.4164 | 1.10756 | ||||||||
\(448\) | 12.0902 | 0.571207 | ||||||||
\(449\) | −15.3262 | −0.723290 | −0.361645 | − | 0.932316i | \(-0.617785\pi\) | ||||
−0.361645 | + | 0.932316i | \(0.617785\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.00000 | −0.141264 | ||||||||
\(452\) | 7.20163 | 0.338736 | ||||||||
\(453\) | 7.85410 | 0.369018 | ||||||||
\(454\) | −38.8885 | −1.82513 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 39.2705 | 1.83901 | ||||||||
\(457\) | 7.97871 | 0.373228 | 0.186614 | − | 0.982433i | \(-0.440249\pi\) | ||||
0.186614 | + | 0.982433i | \(0.440249\pi\) | |||||||
\(458\) | −19.4721 | −0.909873 | ||||||||
\(459\) | −1.38197 | −0.0645046 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.18034 | −0.427571 | −0.213786 | − | 0.976881i | \(-0.568579\pi\) | ||||
−0.213786 | + | 0.976881i | \(0.568579\pi\) | |||||||
\(462\) | 12.0902 | 0.562486 | ||||||||
\(463\) | −11.3607 | −0.527976 | −0.263988 | − | 0.964526i | \(-0.585038\pi\) | ||||
−0.263988 | + | 0.964526i | \(0.585038\pi\) | |||||||
\(464\) | 6.70820 | 0.311421 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.0902 | 1.16228 | ||||||||
\(467\) | −37.4721 | −1.73400 | −0.867002 | − | 0.498305i | \(-0.833956\pi\) | ||||
−0.867002 | + | 0.498305i | \(0.833956\pi\) | |||||||
\(468\) | −14.8541 | −0.686631 | ||||||||
\(469\) | −22.8328 | −1.05432 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.1803 | −0.653396 | ||||||||
\(472\) | 1.18034 | 0.0543295 | ||||||||
\(473\) | 6.00000 | 0.275880 | ||||||||
\(474\) | 24.7984 | 1.13903 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.09017 | 0.0499679 | ||||||||
\(477\) | −35.9443 | −1.64578 | ||||||||
\(478\) | −10.3262 | −0.472311 | ||||||||
\(479\) | 28.4164 | 1.29838 | 0.649189 | − | 0.760627i | \(-0.275108\pi\) | ||||
0.649189 | + | 0.760627i | \(0.275108\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 63.8328 | 2.91053 | ||||||||
\(482\) | −34.4164 | −1.56762 | ||||||||
\(483\) | −30.5623 | −1.39063 | ||||||||
\(484\) | 0.618034 | 0.0280925 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −35.0344 | −1.58919 | ||||||||
\(487\) | 30.4164 | 1.37830 | 0.689150 | − | 0.724619i | \(-0.257984\pi\) | ||||
0.689150 | + | 0.724619i | \(0.257984\pi\) | |||||||
\(488\) | 0.201626 | 0.00912719 | ||||||||
\(489\) | −17.9443 | −0.811468 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.81966 | −0.307767 | −0.153883 | − | 0.988089i | \(-0.549178\pi\) | ||||
−0.153883 | + | 0.988089i | \(0.549178\pi\) | |||||||
\(492\) | 4.85410 | 0.218840 | ||||||||
\(493\) | −0.854102 | −0.0384668 | ||||||||
\(494\) | −67.6869 | −3.04538 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.5623 | 0.653867 | ||||||||
\(497\) | 23.3475 | 1.04728 | ||||||||
\(498\) | 42.9787 | 1.92592 | ||||||||
\(499\) | 29.7984 | 1.33396 | 0.666979 | − | 0.745076i | \(-0.267587\pi\) | ||||
0.666979 | + | 0.745076i | \(0.267587\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.8541 | −0.618956 | ||||||||
\(502\) | 44.1246 | 1.96938 | ||||||||
\(503\) | 6.65248 | 0.296619 | 0.148310 | − | 0.988941i | \(-0.452617\pi\) | ||||
0.148310 | + | 0.988941i | \(0.452617\pi\) | |||||||
\(504\) | 24.5967 | 1.09563 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.61803 | −0.294207 | ||||||||
\(507\) | −67.7771 | −3.01009 | ||||||||
\(508\) | 0.381966 | 0.0169470 | ||||||||
\(509\) | 16.3820 | 0.726118 | 0.363059 | − | 0.931766i | \(-0.381732\pi\) | ||||
0.363059 | + | 0.931766i | \(0.381732\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.6312 | −1.31081 | ||||||||
\(512\) | 5.29180 | 0.233867 | ||||||||
\(513\) | 15.0000 | 0.662266 | ||||||||
\(514\) | −17.7082 | −0.781075 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.70820 | −0.427380 | ||||||||
\(517\) | −11.9443 | −0.525308 | ||||||||
\(518\) | 47.2705 | 2.07695 | ||||||||
\(519\) | −14.3262 | −0.628852 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.81966 | −0.0797208 | −0.0398604 | − | 0.999205i | \(-0.512691\pi\) | ||||
−0.0398604 | + | 0.999205i | \(0.512691\pi\) | |||||||
\(522\) | 8.61803 | 0.377201 | ||||||||
\(523\) | −22.9443 | −1.00328 | −0.501641 | − | 0.865076i | \(-0.667270\pi\) | ||||
−0.501641 | + | 0.865076i | \(0.667270\pi\) | |||||||
\(524\) | 6.23607 | 0.272424 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −33.9787 | −1.48154 | ||||||||
\(527\) | −1.85410 | −0.0807660 | ||||||||
\(528\) | 12.7082 | 0.553054 | ||||||||
\(529\) | −6.27051 | −0.272631 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.03444 | 0.0882873 | ||||||||
\(532\) | −11.8328 | −0.513018 | ||||||||
\(533\) | 18.7082 | 0.810342 | ||||||||
\(534\) | −29.2705 | −1.26666 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −17.8885 | −0.772667 | ||||||||
\(537\) | 35.6525 | 1.53852 | ||||||||
\(538\) | −49.0689 | −2.11551 | ||||||||
\(539\) | 1.14590 | 0.0493573 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.2705 | −1.81735 | −0.908676 | − | 0.417503i | \(-0.862905\pi\) | ||||
−0.908676 | + | 0.417503i | \(0.862905\pi\) | |||||||
\(542\) | −21.3262 | −0.916040 | ||||||||
\(543\) | 15.9443 | 0.684234 | ||||||||
\(544\) | 2.09017 | 0.0896153 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −75.3951 | −3.22661 | ||||||||
\(547\) | 21.1459 | 0.904133 | 0.452067 | − | 0.891984i | \(-0.350687\pi\) | ||||
0.452067 | + | 0.891984i | \(0.350687\pi\) | |||||||
\(548\) | −3.43769 | −0.146851 | ||||||||
\(549\) | 0.347524 | 0.0148320 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.27051 | 0.394937 | ||||||||
\(552\) | −23.9443 | −1.01914 | ||||||||
\(553\) | 16.7082 | 0.710505 | ||||||||
\(554\) | −18.5623 | −0.788637 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.03444 | −0.0862796 | ||||||||
\(557\) | 9.76393 | 0.413711 | 0.206856 | − | 0.978371i | \(-0.433677\pi\) | ||||
0.206856 | + | 0.978371i | \(0.433677\pi\) | |||||||
\(558\) | 18.7082 | 0.791981 | ||||||||
\(559\) | −37.4164 | −1.58255 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.61803 | −0.0683134 | ||||||||
\(562\) | 41.0344 | 1.73093 | ||||||||
\(563\) | 13.0344 | 0.549336 | 0.274668 | − | 0.961539i | \(-0.411432\pi\) | ||||
0.274668 | + | 0.961539i | \(0.411432\pi\) | |||||||
\(564\) | 19.3262 | 0.813781 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11.9443 | −0.502055 | ||||||||
\(567\) | −16.2918 | −0.684191 | ||||||||
\(568\) | 18.2918 | 0.767507 | ||||||||
\(569\) | 26.3820 | 1.10599 | 0.552995 | − | 0.833185i | \(-0.313485\pi\) | ||||
0.552995 | + | 0.833185i | \(0.313485\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.2705 | 1.51787 | 0.758937 | − | 0.651164i | \(-0.225719\pi\) | ||||
0.758937 | + | 0.651164i | \(0.225719\pi\) | |||||||
\(572\) | −3.85410 | −0.161148 | ||||||||
\(573\) | 55.2148 | 2.30663 | ||||||||
\(574\) | 13.8541 | 0.578259 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 16.3262 | 0.680260 | ||||||||
\(577\) | −15.5623 | −0.647867 | −0.323934 | − | 0.946080i | \(-0.605005\pi\) | ||||
−0.323934 | + | 0.946080i | \(0.605005\pi\) | |||||||
\(578\) | 26.8885 | 1.11842 | ||||||||
\(579\) | 33.8885 | 1.40836 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.9574 | 1.20136 | ||||||||
\(582\) | −6.85410 | −0.284112 | ||||||||
\(583\) | −9.32624 | −0.386253 | ||||||||
\(584\) | −23.2148 | −0.960635 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38.6525 | −1.59672 | ||||||||
\(587\) | 4.03444 | 0.166519 | 0.0832596 | − | 0.996528i | \(-0.473467\pi\) | ||||
0.0832596 | + | 0.996528i | \(0.473467\pi\) | |||||||
\(588\) | −1.85410 | −0.0764619 | ||||||||
\(589\) | 20.1246 | 0.829220 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −52.5967 | −2.16354 | ||||||||
\(592\) | 49.6869 | 2.04212 | ||||||||
\(593\) | −9.00000 | −0.369586 | −0.184793 | − | 0.982777i | \(-0.559161\pi\) | ||||
−0.184793 | + | 0.982777i | \(0.559161\pi\) | |||||||
\(594\) | 3.61803 | 0.148450 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.52786 | −0.226430 | ||||||||
\(597\) | 8.09017 | 0.331109 | ||||||||
\(598\) | 41.2705 | 1.68768 | ||||||||
\(599\) | 0.326238 | 0.0133297 | 0.00666486 | − | 0.999978i | \(-0.497878\pi\) | ||||
0.00666486 | + | 0.999978i | \(0.497878\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.2705 | −0.908433 | −0.454217 | − | 0.890891i | \(-0.650081\pi\) | ||||
−0.454217 | + | 0.890891i | \(0.650081\pi\) | |||||||
\(602\) | −27.7082 | −1.12930 | ||||||||
\(603\) | −30.8328 | −1.25561 | ||||||||
\(604\) | −1.85410 | −0.0754423 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −25.7984 | −1.04799 | ||||||||
\(607\) | −3.52786 | −0.143192 | −0.0715958 | − | 0.997434i | \(-0.522809\pi\) | ||||
−0.0715958 | + | 0.997434i | \(0.522809\pi\) | |||||||
\(608\) | −22.6869 | −0.920076 | ||||||||
\(609\) | 10.3262 | 0.418440 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 74.4853 | 3.01335 | ||||||||
\(612\) | 1.47214 | 0.0595076 | ||||||||
\(613\) | −6.43769 | −0.260016 | −0.130008 | − | 0.991513i | \(-0.541500\pi\) | ||||
−0.130008 | + | 0.991513i | \(0.541500\pi\) | |||||||
\(614\) | 54.1246 | 2.18429 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.38197 | 0.257137 | ||||||||
\(617\) | 38.1803 | 1.53708 | 0.768541 | − | 0.639800i | \(-0.220983\pi\) | ||||
0.768541 | + | 0.639800i | \(0.220983\pi\) | |||||||
\(618\) | −22.7984 | −0.917085 | ||||||||
\(619\) | −22.8885 | −0.919968 | −0.459984 | − | 0.887927i | \(-0.652145\pi\) | ||||
−0.459984 | + | 0.887927i | \(0.652145\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.14590 | −0.367012 | ||||||||
\(622\) | 31.0344 | 1.24437 | ||||||||
\(623\) | −19.7214 | −0.790120 | ||||||||
\(624\) | −79.2492 | −3.17251 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.23607 | −0.209275 | ||||||||
\(627\) | 17.5623 | 0.701371 | ||||||||
\(628\) | 3.34752 | 0.133581 | ||||||||
\(629\) | −6.32624 | −0.252244 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.2705 | 1.44391 | 0.721953 | − | 0.691942i | \(-0.243245\pi\) | ||||
0.721953 | + | 0.691942i | \(0.243245\pi\) | |||||||
\(632\) | 13.0902 | 0.520699 | ||||||||
\(633\) | −44.5066 | −1.76898 | ||||||||
\(634\) | 26.8885 | 1.06788 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 15.0902 | 0.598364 | ||||||||
\(637\) | −7.14590 | −0.283131 | ||||||||
\(638\) | 2.23607 | 0.0885268 | ||||||||
\(639\) | 31.5279 | 1.24722 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.00000 | −0.118493 | −0.0592464 | − | 0.998243i | \(-0.518870\pi\) | ||||
−0.0592464 | + | 0.998243i | \(0.518870\pi\) | |||||||
\(642\) | 17.9443 | 0.708204 | ||||||||
\(643\) | −10.5836 | −0.417376 | −0.208688 | − | 0.977982i | \(-0.566919\pi\) | ||||
−0.208688 | + | 0.977982i | \(0.566919\pi\) | |||||||
\(644\) | 7.21478 | 0.284302 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.70820 | 0.263931 | ||||||||
\(647\) | −12.3475 | −0.485431 | −0.242716 | − | 0.970097i | \(-0.578038\pi\) | ||||
−0.242716 | + | 0.970097i | \(0.578038\pi\) | |||||||
\(648\) | −12.7639 | −0.501415 | ||||||||
\(649\) | 0.527864 | 0.0207205 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.4164 | 0.878568 | ||||||||
\(652\) | 4.23607 | 0.165897 | ||||||||
\(653\) | −7.74265 | −0.302993 | −0.151497 | − | 0.988458i | \(-0.548409\pi\) | ||||
−0.151497 | + | 0.988458i | \(0.548409\pi\) | |||||||
\(654\) | −13.0902 | −0.511866 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.5623 | 0.568563 | ||||||||
\(657\) | −40.0132 | −1.56106 | ||||||||
\(658\) | 55.1591 | 2.15032 | ||||||||
\(659\) | 9.27051 | 0.361128 | 0.180564 | − | 0.983563i | \(-0.442208\pi\) | ||||
0.180564 | + | 0.983563i | \(0.442208\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49.1803 | −1.91289 | −0.956447 | − | 0.291907i | \(-0.905710\pi\) | ||||
−0.956447 | + | 0.291907i | \(0.905710\pi\) | |||||||
\(662\) | 31.0344 | 1.20619 | ||||||||
\(663\) | 10.0902 | 0.391870 | ||||||||
\(664\) | 22.6869 | 0.880423 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 63.8328 | 2.47347 | ||||||||
\(667\) | −5.65248 | −0.218865 | ||||||||
\(668\) | 3.27051 | 0.126540 | ||||||||
\(669\) | 44.2148 | 1.70944 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0901699 | 0.00348097 | ||||||||
\(672\) | −25.2705 | −0.974831 | ||||||||
\(673\) | −2.41641 | −0.0931457 | −0.0465728 | − | 0.998915i | \(-0.514830\pi\) | ||||
−0.0465728 | + | 0.998915i | \(0.514830\pi\) | |||||||
\(674\) | 2.29180 | 0.0882767 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.0000 | 0.615385 | ||||||||
\(677\) | −28.6525 | −1.10120 | −0.550602 | − | 0.834768i | \(-0.685602\pi\) | ||||
−0.550602 | + | 0.834768i | \(0.685602\pi\) | |||||||
\(678\) | 49.3607 | 1.89569 | ||||||||
\(679\) | −4.61803 | −0.177224 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −62.9230 | −2.41121 | ||||||||
\(682\) | 4.85410 | 0.185873 | ||||||||
\(683\) | 43.3607 | 1.65915 | 0.829575 | − | 0.558395i | \(-0.188583\pi\) | ||||
0.829575 | + | 0.558395i | \(0.188583\pi\) | |||||||
\(684\) | −15.9787 | −0.610961 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 27.0344 | 1.03218 | ||||||||
\(687\) | −31.5066 | −1.20205 | ||||||||
\(688\) | −29.1246 | −1.11037 | ||||||||
\(689\) | 58.1591 | 2.21568 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.0902 | 1.14468 | 0.572342 | − | 0.820015i | \(-0.306035\pi\) | ||||
0.572342 | + | 0.820015i | \(0.306035\pi\) | |||||||
\(692\) | 3.38197 | 0.128563 | ||||||||
\(693\) | 11.0000 | 0.417855 | ||||||||
\(694\) | 33.2705 | 1.26293 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.09017 | 0.306657 | ||||||||
\(697\) | −1.85410 | −0.0702291 | ||||||||
\(698\) | −35.3262 | −1.33712 | ||||||||
\(699\) | 40.5967 | 1.53551 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.360680 | −0.0136227 | −0.00681134 | − | 0.999977i | \(-0.502168\pi\) | ||||
−0.00681134 | + | 0.999977i | \(0.502168\pi\) | |||||||
\(702\) | −22.5623 | −0.851559 | ||||||||
\(703\) | 68.6656 | 2.58977 | ||||||||
\(704\) | 4.23607 | 0.159653 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 34.5623 | 1.30077 | ||||||||
\(707\) | −17.3820 | −0.653716 | ||||||||
\(708\) | −0.854102 | −0.0320991 | ||||||||
\(709\) | −41.3050 | −1.55124 | −0.775620 | − | 0.631200i | \(-0.782563\pi\) | ||||
−0.775620 | + | 0.631200i | \(0.782563\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.5623 | 0.846153 | ||||||||
\(712\) | −15.4508 | −0.579045 | ||||||||
\(713\) | −12.2705 | −0.459534 | ||||||||
\(714\) | 7.47214 | 0.279638 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.41641 | −0.314536 | ||||||||
\(717\) | −16.7082 | −0.623979 | ||||||||
\(718\) | 7.23607 | 0.270048 | ||||||||
\(719\) | −15.6525 | −0.583739 | −0.291869 | − | 0.956458i | \(-0.594277\pi\) | ||||
−0.291869 | + | 0.956458i | \(0.594277\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.3607 | −0.572062 | ||||||||
\(722\) | −42.0689 | −1.56564 | ||||||||
\(723\) | −55.6869 | −2.07102 | ||||||||
\(724\) | −3.76393 | −0.139885 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.23607 | 0.157215 | ||||||||
\(727\) | 41.2705 | 1.53064 | 0.765319 | − | 0.643651i | \(-0.222581\pi\) | ||||
0.765319 | + | 0.643651i | \(0.222581\pi\) | |||||||
\(728\) | −39.7984 | −1.47503 | ||||||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.70820 | 0.137153 | ||||||||
\(732\) | −0.145898 | −0.00539255 | ||||||||
\(733\) | −45.8328 | −1.69287 | −0.846437 | − | 0.532489i | \(-0.821257\pi\) | ||||
−0.846437 | + | 0.532489i | \(0.821257\pi\) | |||||||
\(734\) | 11.5623 | 0.426772 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.8328 | 0.509884 | ||||||||
\(737\) | −8.00000 | −0.294684 | ||||||||
\(738\) | 18.7082 | 0.688659 | ||||||||
\(739\) | −29.1459 | −1.07215 | −0.536075 | − | 0.844171i | \(-0.680093\pi\) | ||||
−0.536075 | + | 0.844171i | \(0.680093\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −109.520 | −4.02331 | ||||||||
\(742\) | 43.0689 | 1.58111 | ||||||||
\(743\) | −18.6738 | −0.685074 | −0.342537 | − | 0.939504i | \(-0.611286\pi\) | ||||
−0.342537 | + | 0.939504i | \(0.611286\pi\) | |||||||
\(744\) | 17.5623 | 0.643865 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.56231 | 0.167038 | ||||||||
\(747\) | 39.1033 | 1.43072 | ||||||||
\(748\) | 0.381966 | 0.0139661 | ||||||||
\(749\) | 12.0902 | 0.441765 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.2705 | 0.411267 | 0.205633 | − | 0.978629i | \(-0.434075\pi\) | ||||
0.205633 | + | 0.978629i | \(0.434075\pi\) | |||||||
\(752\) | 57.9787 | 2.11427 | ||||||||
\(753\) | 71.3951 | 2.60178 | ||||||||
\(754\) | −13.9443 | −0.507820 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.94427 | −0.143452 | ||||||||
\(757\) | 21.4721 | 0.780418 | 0.390209 | − | 0.920726i | \(-0.372403\pi\) | ||||
0.390209 | + | 0.920726i | \(0.372403\pi\) | |||||||
\(758\) | 28.7426 | 1.04398 | ||||||||
\(759\) | −10.7082 | −0.388683 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.0000 | 0.435000 | 0.217500 | − | 0.976060i | \(-0.430210\pi\) | ||||
0.217500 | + | 0.976060i | \(0.430210\pi\) | |||||||
\(762\) | 2.61803 | 0.0948414 | ||||||||
\(763\) | −8.81966 | −0.319293 | ||||||||
\(764\) | −13.0344 | −0.471570 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.18034 | 0.295568 | ||||||||
\(767\) | −3.29180 | −0.118860 | ||||||||
\(768\) | −35.5066 | −1.28123 | ||||||||
\(769\) | −5.00000 | −0.180305 | −0.0901523 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901523 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.6525 | −1.03189 | ||||||||
\(772\) | −8.00000 | −0.287926 | ||||||||
\(773\) | −33.7984 | −1.21564 | −0.607822 | − | 0.794074i | \(-0.707956\pi\) | ||||
−0.607822 | + | 0.794074i | \(0.707956\pi\) | |||||||
\(774\) | −37.4164 | −1.34491 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.61803 | −0.129880 | ||||||||
\(777\) | 76.4853 | 2.74389 | ||||||||
\(778\) | −8.94427 | −0.320668 | ||||||||
\(779\) | 20.1246 | 0.721039 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.18034 | 0.292716 | ||||||||
\(782\) | −4.09017 | −0.146264 | ||||||||
\(783\) | 3.09017 | 0.110434 | ||||||||
\(784\) | −5.56231 | −0.198654 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 42.7426 | 1.52458 | ||||||||
\(787\) | −21.2918 | −0.758971 | −0.379485 | − | 0.925198i | \(-0.623899\pi\) | ||||
−0.379485 | + | 0.925198i | \(0.623899\pi\) | |||||||
\(788\) | 12.4164 | 0.442316 | ||||||||
\(789\) | −54.9787 | −1.95729 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.2574 | 1.18250 | ||||||||
\(792\) | 8.61803 | 0.306229 | ||||||||
\(793\) | −0.562306 | −0.0199681 | ||||||||
\(794\) | 24.1246 | 0.856150 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.90983 | −0.0676921 | ||||||||
\(797\) | −3.20163 | −0.113407 | −0.0567037 | − | 0.998391i | \(-0.518059\pi\) | ||||
−0.0567037 | + | 0.998391i | \(0.518059\pi\) | |||||||
\(798\) | −81.1033 | −2.87103 | ||||||||
\(799\) | −7.38197 | −0.261155 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −26.6312 | −0.940967 | ||||||||
\(802\) | −55.5967 | −1.96319 | ||||||||
\(803\) | −10.3820 | −0.366372 | ||||||||
\(804\) | 12.9443 | 0.456509 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −30.2705 | −1.06623 | ||||||||
\(807\) | −79.3951 | −2.79484 | ||||||||
\(808\) | −13.6180 | −0.479081 | ||||||||
\(809\) | −16.5836 | −0.583048 | −0.291524 | − | 0.956564i | \(-0.594162\pi\) | ||||
−0.291524 | + | 0.956564i | \(0.594162\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.0000 | 0.596951 | 0.298475 | − | 0.954417i | \(-0.403522\pi\) | ||||
0.298475 | + | 0.954417i | \(0.403522\pi\) | |||||||
\(812\) | −2.43769 | −0.0855463 | ||||||||
\(813\) | −34.5066 | −1.21020 | ||||||||
\(814\) | 16.5623 | 0.580509 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.85410 | 0.274949 | ||||||||
\(817\) | −40.2492 | −1.40814 | ||||||||
\(818\) | −32.5623 | −1.13851 | ||||||||
\(819\) | −68.5967 | −2.39696 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.36068 | 0.152189 | 0.0760944 | − | 0.997101i | \(-0.475755\pi\) | ||||
0.0760944 | + | 0.997101i | \(0.475755\pi\) | |||||||
\(822\) | −23.5623 | −0.821830 | ||||||||
\(823\) | −27.4164 | −0.955676 | −0.477838 | − | 0.878448i | \(-0.658579\pi\) | ||||
−0.477838 | + | 0.878448i | \(0.658579\pi\) | |||||||
\(824\) | −12.0344 | −0.419240 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.43769 | −0.0848182 | ||||||||
\(827\) | −32.0689 | −1.11514 | −0.557572 | − | 0.830128i | \(-0.688267\pi\) | ||||
−0.557572 | + | 0.830128i | \(0.688267\pi\) | |||||||
\(828\) | 9.74265 | 0.338580 | ||||||||
\(829\) | −36.1033 | −1.25392 | −0.626960 | − | 0.779051i | \(-0.715701\pi\) | ||||
−0.626960 | + | 0.779051i | \(0.715701\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.0344 | −1.04188 | ||||||||
\(832\) | −26.4164 | −0.915824 | ||||||||
\(833\) | 0.708204 | 0.0245378 | ||||||||
\(834\) | −13.9443 | −0.482851 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.14590 | −0.143389 | ||||||||
\(837\) | 6.70820 | 0.231869 | ||||||||
\(838\) | −34.2705 | −1.18386 | ||||||||
\(839\) | −48.3394 | −1.66886 | −0.834431 | − | 0.551113i | \(-0.814203\pi\) | ||||
−0.834431 | + | 0.551113i | \(0.814203\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0902 | −0.934144 | ||||||||
\(842\) | 19.8541 | 0.684218 | ||||||||
\(843\) | 66.3951 | 2.28677 | ||||||||
\(844\) | 10.5066 | 0.361651 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 74.4853 | 2.56086 | ||||||||
\(847\) | 2.85410 | 0.0980681 | ||||||||
\(848\) | 45.2705 | 1.55460 | ||||||||
\(849\) | −19.3262 | −0.663275 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −41.8673 | −1.43519 | ||||||||
\(852\) | −13.2361 | −0.453460 | ||||||||
\(853\) | −49.8541 | −1.70697 | −0.853486 | − | 0.521116i | \(-0.825516\pi\) | ||||
−0.853486 | + | 0.521116i | \(0.825516\pi\) | |||||||
\(854\) | −0.416408 | −0.0142492 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.47214 | 0.323751 | ||||||||
\(857\) | 53.1803 | 1.81661 | 0.908303 | − | 0.418313i | \(-0.137379\pi\) | ||||
0.908303 | + | 0.418313i | \(0.137379\pi\) | |||||||
\(858\) | −26.4164 | −0.901841 | ||||||||
\(859\) | 16.1803 | 0.552066 | 0.276033 | − | 0.961148i | \(-0.410980\pi\) | ||||
0.276033 | + | 0.961148i | \(0.410980\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.4164 | 0.763949 | ||||||||
\(862\) | −1.32624 | −0.0451718 | ||||||||
\(863\) | 0.596748 | 0.0203135 | 0.0101568 | − | 0.999948i | \(-0.496767\pi\) | ||||
0.0101568 | + | 0.999948i | \(0.496767\pi\) | |||||||
\(864\) | −7.56231 | −0.257275 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −30.5623 | −1.03855 | ||||||||
\(867\) | 43.5066 | 1.47756 | ||||||||
\(868\) | −5.29180 | −0.179615 | ||||||||
\(869\) | 5.85410 | 0.198587 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.8885 | 1.69041 | ||||||||
\(872\) | −6.90983 | −0.233996 | ||||||||
\(873\) | −6.23607 | −0.211059 | ||||||||
\(874\) | 44.3951 | 1.50169 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.7984 | 0.567564 | ||||||||
\(877\) | −4.58359 | −0.154777 | −0.0773885 | − | 0.997001i | \(-0.524658\pi\) | ||||
−0.0773885 | + | 0.997001i | \(0.524658\pi\) | |||||||
\(878\) | 1.18034 | 0.0398345 | ||||||||
\(879\) | −62.5410 | −2.10946 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.0902 | 0.339946 | 0.169973 | − | 0.985449i | \(-0.445632\pi\) | ||||
0.169973 | + | 0.985449i | \(0.445632\pi\) | |||||||
\(882\) | −7.14590 | −0.240615 | ||||||||
\(883\) | 31.6525 | 1.06519 | 0.532595 | − | 0.846370i | \(-0.321217\pi\) | ||||
0.532595 | + | 0.846370i | \(0.321217\pi\) | |||||||
\(884\) | −2.38197 | −0.0801142 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −59.3050 | −1.99239 | ||||||||
\(887\) | −28.7771 | −0.966240 | −0.483120 | − | 0.875554i | \(-0.660497\pi\) | ||||
−0.483120 | + | 0.875554i | \(0.660497\pi\) | |||||||
\(888\) | 59.9230 | 2.01088 | ||||||||
\(889\) | 1.76393 | 0.0591604 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.70820 | −0.191232 | ||||||||
\(892\) | −10.4377 | −0.349480 | ||||||||
\(893\) | 80.1246 | 2.68127 | ||||||||
\(894\) | −37.8885 | −1.26718 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −38.8673 | −1.29846 | ||||||||
\(897\) | 66.7771 | 2.22962 | ||||||||
\(898\) | 24.7984 | 0.827532 | ||||||||
\(899\) | 4.14590 | 0.138273 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.76393 | −0.192024 | ||||||||
\(902\) | 4.85410 | 0.161624 | ||||||||
\(903\) | −44.8328 | −1.49194 | ||||||||
\(904\) | 26.0557 | 0.866601 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −12.7082 | −0.422202 | ||||||||
\(907\) | −14.8328 | −0.492516 | −0.246258 | − | 0.969204i | \(-0.579201\pi\) | ||||
−0.246258 | + | 0.969204i | \(0.579201\pi\) | |||||||
\(908\) | 14.8541 | 0.492951 | ||||||||
\(909\) | −23.4721 | −0.778522 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.0000 | −0.596367 | −0.298183 | − | 0.954509i | \(-0.596381\pi\) | ||||
−0.298183 | + | 0.954509i | \(0.596381\pi\) | |||||||
\(912\) | −85.2492 | −2.82288 | ||||||||
\(913\) | 10.1459 | 0.335780 | ||||||||
\(914\) | −12.9098 | −0.427019 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.43769 | 0.245748 | ||||||||
\(917\) | 28.7984 | 0.951006 | ||||||||
\(918\) | 2.23607 | 0.0738012 | ||||||||
\(919\) | 23.4164 | 0.772436 | 0.386218 | − | 0.922408i | \(-0.373781\pi\) | ||||
0.386218 | + | 0.922408i | \(0.373781\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 87.5755 | 2.88571 | ||||||||
\(922\) | 14.8541 | 0.489194 | ||||||||
\(923\) | −51.0132 | −1.67912 | ||||||||
\(924\) | −4.61803 | −0.151922 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.3820 | 0.604069 | ||||||||
\(927\) | −20.7426 | −0.681278 | ||||||||
\(928\) | −4.67376 | −0.153424 | ||||||||
\(929\) | 54.5967 | 1.79126 | 0.895631 | − | 0.444799i | \(-0.146725\pi\) | ||||
0.895631 | + | 0.444799i | \(0.146725\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.68692 | −0.251929 | ||||||||
\(932\) | −9.58359 | −0.313921 | ||||||||
\(933\) | 50.2148 | 1.64396 | ||||||||
\(934\) | 60.6312 | 1.98391 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −53.7426 | −1.75663 | ||||||||
\(937\) | 38.8328 | 1.26861 | 0.634306 | − | 0.773082i | \(-0.281286\pi\) | ||||
0.634306 | + | 0.773082i | \(0.281286\pi\) | |||||||
\(938\) | 36.9443 | 1.20627 | ||||||||
\(939\) | −8.47214 | −0.276478 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.7214 | 1.36008 | 0.680039 | − | 0.733176i | \(-0.261963\pi\) | ||||
0.680039 | + | 0.733176i | \(0.261963\pi\) | |||||||
\(942\) | 22.9443 | 0.747565 | ||||||||
\(943\) | −12.2705 | −0.399583 | ||||||||
\(944\) | −2.56231 | −0.0833960 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.70820 | −0.315641 | ||||||||
\(947\) | 39.3607 | 1.27905 | 0.639525 | − | 0.768770i | \(-0.279131\pi\) | ||||
0.639525 | + | 0.768770i | \(0.279131\pi\) | |||||||
\(948\) | −9.47214 | −0.307641 | ||||||||
\(949\) | 64.7426 | 2.10164 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43.5066 | 1.41080 | ||||||||
\(952\) | 3.94427 | 0.127835 | ||||||||
\(953\) | −8.47214 | −0.274439 | −0.137220 | − | 0.990541i | \(-0.543817\pi\) | ||||
−0.137220 | + | 0.990541i | \(0.543817\pi\) | |||||||
\(954\) | 58.1591 | 1.88297 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.94427 | 0.127567 | ||||||||
\(957\) | 3.61803 | 0.116954 | ||||||||
\(958\) | −45.9787 | −1.48550 | ||||||||
\(959\) | −15.8754 | −0.512643 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | −103.284 | −3.33000 | ||||||||
\(963\) | 16.3262 | 0.526106 | ||||||||
\(964\) | 13.1459 | 0.423401 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 49.4508 | 1.59106 | ||||||||
\(967\) | −37.2705 | −1.19854 | −0.599269 | − | 0.800547i | \(-0.704542\pi\) | ||||
−0.599269 | + | 0.800547i | \(0.704542\pi\) | |||||||
\(968\) | 2.23607 | 0.0718699 | ||||||||
\(969\) | 10.8541 | 0.348684 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.9098 | 0.767303 | 0.383651 | − | 0.923478i | \(-0.374666\pi\) | ||||
0.383651 | + | 0.923478i | \(0.374666\pi\) | |||||||
\(972\) | 13.3820 | 0.429227 | ||||||||
\(973\) | −9.39512 | −0.301194 | ||||||||
\(974\) | −49.2148 | −1.57694 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.437694 | −0.0140102 | ||||||||
\(977\) | −57.0689 | −1.82580 | −0.912898 | − | 0.408188i | \(-0.866161\pi\) | ||||
−0.912898 | + | 0.408188i | \(0.866161\pi\) | |||||||
\(978\) | 29.0344 | 0.928419 | ||||||||
\(979\) | −6.90983 | −0.220839 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.9098 | −0.380252 | ||||||||
\(982\) | 11.0344 | 0.352123 | ||||||||
\(983\) | 1.52786 | 0.0487313 | 0.0243656 | − | 0.999703i | \(-0.492243\pi\) | ||||
0.0243656 | + | 0.999703i | \(0.492243\pi\) | |||||||
\(984\) | 17.5623 | 0.559866 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.38197 | 0.0440108 | ||||||||
\(987\) | 89.2492 | 2.84083 | ||||||||
\(988\) | 25.8541 | 0.822529 | ||||||||
\(989\) | 24.5410 | 0.780359 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.2705 | 0.675680 | 0.337840 | − | 0.941204i | \(-0.390304\pi\) | ||||
0.337840 | + | 0.941204i | \(0.390304\pi\) | |||||||
\(992\) | −10.1459 | −0.322133 | ||||||||
\(993\) | 50.2148 | 1.59352 | ||||||||
\(994\) | −37.7771 | −1.19822 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −16.4164 | −0.520174 | ||||||||
\(997\) | −32.1459 | −1.01807 | −0.509035 | − | 0.860746i | \(-0.669998\pi\) | ||||
−0.509035 | + | 0.860746i | \(0.669998\pi\) | |||||||
\(998\) | −48.2148 | −1.52621 | ||||||||
\(999\) | 22.8885 | 0.724161 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 275.2.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 2475.2.a.s.1.2 | 2 | |||
4.3 | odd | 2 | 4400.2.a.bv.1.2 | 2 | |||
5.2 | odd | 4 | 275.2.b.e.199.1 | 4 | |||
5.3 | odd | 4 | 275.2.b.e.199.4 | 4 | |||
5.4 | even | 2 | 275.2.a.g.1.2 | yes | 2 | ||
11.10 | odd | 2 | 3025.2.a.m.1.2 | 2 | |||
15.2 | even | 4 | 2475.2.c.p.199.4 | 4 | |||
15.8 | even | 4 | 2475.2.c.p.199.1 | 4 | |||
15.14 | odd | 2 | 2475.2.a.n.1.1 | 2 | |||
20.3 | even | 4 | 4400.2.b.x.4049.4 | 4 | |||
20.7 | even | 4 | 4400.2.b.x.4049.1 | 4 | |||
20.19 | odd | 2 | 4400.2.a.bg.1.1 | 2 | |||
55.54 | odd | 2 | 3025.2.a.i.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
275.2.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
275.2.a.g.1.2 | yes | 2 | 5.4 | even | 2 | ||
275.2.b.e.199.1 | 4 | 5.2 | odd | 4 | |||
275.2.b.e.199.4 | 4 | 5.3 | odd | 4 | |||
2475.2.a.n.1.1 | 2 | 15.14 | odd | 2 | |||
2475.2.a.s.1.2 | 2 | 3.2 | odd | 2 | |||
2475.2.c.p.199.1 | 4 | 15.8 | even | 4 | |||
2475.2.c.p.199.4 | 4 | 15.2 | even | 4 | |||
3025.2.a.i.1.1 | 2 | 55.54 | odd | 2 | |||
3025.2.a.m.1.2 | 2 | 11.10 | odd | 2 | |||
4400.2.a.bg.1.1 | 2 | 20.19 | odd | 2 | |||
4400.2.a.bv.1.2 | 2 | 4.3 | odd | 2 | |||
4400.2.b.x.4049.1 | 4 | 20.7 | even | 4 | |||
4400.2.b.x.4049.4 | 4 | 20.3 | even | 4 |